3 You are doing an industry analysis of the Bloomington pizza industry. The rate (per year) at which pizza restaurants enter the industry is given by p, where p  price of a pizza in dollars. The price of a pizza is assumed to be max(0, 16  .5F), where F  number of pizza restaurants in Bloomington. During a given year, the probability that a pizza restaurant fails is 1/(10  p). Create a birth–death model of this situation.

a In the steady state, estimate the average number of pizza restaurants in Bloomington.

b What fraction of the time will there be more than 20 pizza restaurants in Bloomington?